refs.bib

@misc{million2007,
    title        = {The Hadamard Product},
    author       = {Elizabeth Million},
    year         = {2007},
    howpublished = {\url{http://buzzard.ups.edu/courses/2007spring/projects/million-paper.pdf}}
}

@book{Strang2016,
  author = {Gilbert Strang},
  title  = {Introduction to Linear Algebra},
  year   = {2016}
}

@incollection{Rote2001,
  title     = {Division-free algorithms for the determinant and the pfaffian: algebraic and combinatorial approaches},
  author    = {Rote, G{\"u}nter},
  booktitle = {Computational discrete mathematics},
  pages     = {119--135},
  year      = {2001},
  publisher = {Springer}
}

@article{Strassen1969,
  title     = {Gaussian elimination is not optimal},
  author    = {Strassen, Volker},
  journal   = {Numerische mathematik},
  volume    = {13},
  number    = {4},
  pages     = {354--356},
  year      = {1969},
  publisher = {Springer}
}

@article{Bareiss1968,
 ISSN      = {00255718, 10886842},
 URL       = {http://www.jstor.org/stable/2004533},
 abstract  = {A method is developed which permits integer-preserving elimination in systems of linear equations, AX = B, such that (a) the magnitudes of the coefficients in the transformed matrices are minimized, and (b) the computational efficiency is considerably increased in comparison with the corresponding ordinary (single-step) Gaussian elimination. The algorithms presented can also be used for the efficient evaluation of determinants and their leading minors. Explicit algorithms and flow charts are given for the two-step method. The method should also prove superior to the widely used fraction-producing Gaussian elimination when A is nearly singular.},
 author    = {Erwin H. Bareiss},
 journal   = {Mathematics of Computation},
 number    = {103},
 pages     = {565--578},
 publisher = {American Mathematical Society},
 title     = {Sylvester's Identity and Multistep Integer-Preserving Gaussian Elimination},
 volume    = {22},
 year      = {1968},
 doi       = {10.2307/2004533}
}

@article{Copper1990,
title    = "Matrix multiplication via arithmetic progressions",
journal  = "Journal of Symbolic Computation",
volume   = "9",
number   = "3",
pages    = "251 - 280",
year     = "1990",
note     = "Computational algebraic complexity editorial",
issn     = "0747-7171",
doi      = "10.1016/S0747-7171(08)80013-2",
url      = "http://www.sciencedirect.com/science/article/pii/S0747717108800132",
author   = "Don Coppersmith and Shmuel Winograd",
abstract = "We present a new method for accelerating matrix multiplication asymptotically. Thiswork builds on recent ideas of Volker Strassen, by using a basic trilinear form which is not a matrix product. We make novel use of the Salem-Spencer Theorem, which gives a fairly dense set of integers with no three-term arithmetic progression. Our resulting matrix exponent is 2.376."
}

@inproceedings{LeGall2014,
 author    = {Le Gall, Fran\c{c}ois},
 title     = {Powers of Tensors and Fast Matrix Multiplication},
 booktitle = {Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation},
 series    = {ISSAC '14},
 year      = {2014},
 isbn      = {978-1-4503-2501-1},
 location  = {Kobe, Japan},
 pages     = {296--303},
 numpages  = {8},
 url       = {http://doi.acm.org/10.1145/2608628.2608664},
 doi       = {10.1145/2608628.2608664},
 acmid     = {2608664},
 publisher = {ACM},
 address   = {New York, NY, USA},
 keywords  = {algebraic complexity theory, matrix multiplication},
}

@inproceedings{Williams2012,
 author    = {Williams, Virginia Vassilevska},
 title     = {Multiplying Matrices Faster Than Coppersmith-Winograd},
 booktitle = {Proceedings of the Forty-fourth Annual ACM Symposium on Theory of Computing},
 series    = {STOC '12},
 year      = {2012},
 isbn      = {978-1-4503-1245-5},
 location  = {New York, New York, USA},
 pages     = {887--898},
 numpages  = {12},
 url       = {http://doi.acm.org/10.1145/2213977.2214056},
 doi       = {10.1145/2213977.2214056},
 acmid     = {2214056},
 publisher = {ACM},
 address   = {New York, NY, USA},
 keywords  = {matrix multiplication},
}

@inproceedings{Pan1978,
  title        = {Strassen's algorithm is not optimal trilinear technique of aggregating, uniting and canceling for constructing fast algorithms for matrix operations},
  author       = {Pan, V Ya},
  booktitle    = {Foundations of Computer Science, 1978., 19th Annual Symposium on},
  pages        = {166--176},
  year         = {1978},
  organization = {IEEE},
  doi          = {10.1109/SFCS.1978.34}
}

@article{Bini1979,
  title   = {$O(N^{2.7799})$ COMPLEXITY FOR N BY N APPROXIMATE MATRIX MULTIPLICATION},
  author  = {Bini, DARIO ANDREA and Capovani, Milvio and Romani, Francesco and Lotti, Grazia},
  journal = {Information processing letters},
  volume  = {8},
  number  = {5},
  pages   = {234--235},
  year    = {1979}
}

@article{Schonhage1981,
  title     = {Partial and total matrix multiplication},
  author    = {Sch{\"o}nhage, Arnold},
  journal   = {SIAM Journal on Computing},
  volume    = {10},
  number    = {3},
  pages     = {434--455},
  year      = {1981},
  publisher = {SIAM}
}

@article{Romani1982,
  title     = {Some properties of disjoint sums of tensors related to matrix multiplication},
  author    = {Romani, Francesco},
  journal   = {SIAM Journal on Computing},
  volume    = {11},
  number    = {2},
  pages     = {263--267},
  year      = {1982},
  publisher = {SIAM}
}

@inproceedings{Strassen1986,
  title        = {The asymptotic spectrum of tensors and the exponent of matrix multiplication},
  author       = {Strassen, Volker},
  booktitle    = {Foundations of Computer Science, 1986., 27th Annual Symposium on},
  pages        = {49--54},
  year         = {1986},
  organization = {IEEE}
}

@article{Coppersmith1982,
  title     = {On the asymptotic complexity of matrix multiplication},
  author    = {Coppersmith, Don and Winograd, Shmuel},
  journal   = {SIAM Journal on Computing},
  volume    = {11},
  number    = {3},
  pages     = {472--492},
  year      = {1982},
  publisher = {SIAM}
}

@misc{Minka2000,
  title        = {Old and new matrix algebra useful for statistics},
  author       = {Minka, Thomas P},
  howpublished = {\url{https://tminka.github.io/papers/matrix/minka-matrix.pdf}},
  year         = {2000}
}

@book{Calafiore2014,
  title     = {Optimization models},
  author    = {Calafiore, Giuseppe C and El Ghaoui, Laurent},
  year      = {2014},
  publisher = {Cambridge University Press},
  isbn      = {978-1-107-05087-7}
}



















@article{Charnes1962,
author  = {Charnes, A. and Cooper, W. W.},
title   = {Programming with linear fractional functionals},
journal = {Naval Research Logistics Quarterly},
volume  = {9},
year    = {1962},
number  = {3‐4},
pages   = {181-186},
doi     = {10.1002/nav.3800090303},
url     = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nav.3800090303},
eprint  = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/nav.3800090303}
}



@article{Lobo1998,
  title     = {Applications of second-order cone programming},
  author    = {Lobo, Miguel Sousa and Vandenberghe, Lieven and Boyd, Stephen and Lebret, Herv{\'e}},
  journal   = {Linear algebra and its applications},
  volume    = {284},
  number    = {1-3},
  pages     = {193--228},
  year      = {1998},
  publisher = {Elsevier}
}


@article{Thome2016,
  title     = {Inequalities and equalities for l=2 ({S}ylvester), l=3 ({F}robenius), and l>3 matrices},
  author    = {Thome, N{\'e}stor},
  journal   = {Aequationes mathematicae},
  volume    = {90},
  number    = {5},
  pages     = {951--960},
  year      = {2016},
  publisher = {Springer}
}

@article{Sylvester1851,
  title     = {XXXVII. On the relation between the minor determinants of linearly equivalent quadratic functions},
  author    = {Sylvester, James Joseph},
  journal   = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science},
  volume    = {1},
  number    = {4},
  pages     = {295--305},
  year      = {1851},
  publisher = {Taylor \& Francis}
}

@article{Kozlov1980,
  title     = {The polynomial solvability of convex quadratic programming},
  author    = {Kozlov, Mikhail K and Tarasov, Sergei P and Khachiyan, Leonid G},
  journal   = {USSR Computational Mathematics and Mathematical Physics},
  volume    = {20},
  number    = {5},
  pages     = {223--228},
  year      = {1980},
  publisher = {Elsevier}
}


@article{Sahni1974,
  author  = {Sahni, S.},
  title   = {Computationally Related Problems},
  journal = {SIAM Journal on Computing},
  volume  = {3},
  number  = {4},
  pages   = {262-279},
  year    = {1974},
  doi     = {10.1137/0203021},
  URL     = {https://doi.org/10.1137/0203021},
  eprint  = {https://doi.org/10.1137/0203021}
}

@article{Pardalos1991,
  author   = "Pardalos, Panos M. and Vavasis, Stephen A.",
  title    = "Quadratic programming with one negative eigenvalue is NP-hard",
  journal  = "Journal of Global Optimization",
  year     = "1991",
  month    = "Mar",
  day      = "01",
  volume   = "1",
  number   = "1",
  pages    = "15--22",
  abstract = "We show that the problem of minimizing a concave quadratic function with one concave direction is NP-hard. This result can be interpreted as an attempt to understand exactly what makes nonconvex quadratic programming problems hard. Sahni in 1974 [8] showed that quadratic programming with a negative definite quadratic term (n negative eigenvalues) is NP-hard, whereas Kozlov, Tarasov and Ha{\v{c}}ijan [2] showed in 1979 that the ellipsoid algorithm solves the convex quadratic problem (no negative eigenvalues) in polynomial time. This report shows that even one negative eigenvalue makes the problem NP-hard.",
  issn     = "1573-2916",
  doi      = "10.1007/BF00120662",
  url      = "https://doi.org/10.1007/BF00120662"
}


@inproceedings{Spielman2010,
  title     = {Algorithms, graph theory, and linear equations in {Laplacian} matrices},
  volume    = {4},
  url       = {http://www.cs.yale.edu/homes/spielman/PAPERS/icm10post.pdf},
  urldate   = {2016-05-07},
  booktitle = {Proceedings of the {International} {Congress} of {Mathematicians}},
  author    = {Spielman, Daniel A.},
  year      = {2010},
  pages     = {2698--2722},
  file      = {10.1.1.165.8870.pdf:/home/rick/Zotero/storage/XKEEGKW6/10.1.1.165.8870.pdf:application/pdf}
}

@book{Higham2002,
  author    = {Nicholas J. Higham},
  title     = {Accuracy and Stability of Numerical Algorithms},
  edition   = {Second},
  publisher = {SIAM},
  isbn      = {978-0-89871-802-7},
  year      = {2002}
}

@book{Quateroni2007,
  author    = {Quarteroni, Alfio and Sacco, Riccardo and Saleri, Fausto},
  year      = {2007},
  title     = {Numerical Mathematics},
  publisher = {Springer},
  isbn      = {978-3-540-34658-6}
}

@book{Gallopoulos2016,
  author    = {Gallopoulos, E. and Philippe, B. and Sameh, A.H.},
  year      = {2016},
  title     = {Parallelism in Matrix Computations},
  publisher = {Springer},
  isbn      = {978-94-017-7188-7}
}

@Article{Alizadeh2003,
author  = {Alizadeh, F. and Goldfarb, D.},
title   = {Second-order cone programming},
journal = {Mathematical Programming},
year    = {2003},
month   = {Jan},
day     = {01},
volume  = {95},
number  = {1},
pages   = {3-51},
issn    = {1436-4646},
doi     = {10.1007/s10107-002-0339-5},
url     = {https://doi.org/10.1007/s10107-002-0339-5}
}


@article{Teran2011,
  title   = {Consistency and efficient solution of the Sylvester equation for*-congruence},
  author  = {De Ter{\'a}n, Fernando and Dopico, Froilan},
  journal = {The Electronic Journal of Linear Algebra},
  volume  = {22},
  year    = {2011}
}

@article{Teran2019,
author   = {De Terán, Fernando and Iannazzo, Bruno and Poloni, Federico and Robol, Leonardo},
title    = {Nonsingular systems of generalized Sylvester equations: An algorithmic approach},
journal  = {Numerical Linear Algebra with Applications},
volume   = {26},
number   = {5},
pages    = {e2261},
keywords = {formal matrix product, matrix pencils, periodic QR/QZ algorithm, periodic Schur decomposition, Sylvester and ⋆-Sylvester equations, systems of linear matrix equations},
doi      = {https://doi.org/10.1002/nla.2261},
url      = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nla.2261},
eprint   = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/nla.2261},
note     = {e2261 nla.2261},
abstract = {Summary We consider the uniqueness of solution (i.e., nonsingularity) of systems of r generalized Sylvester and ⋆-Sylvester equations with n×n coefficients. After several reductions, we show that it is sufficient to analyze periodic systems having, at most, one generalized ⋆-Sylvester equation. We provide characterizations for the nonsingularity in terms of spectral properties of either matrix pencils or formal matrix products, both constructed from the coefficients of the system. The proposed approach uses the periodic Schur decomposition and leads to a backward stable O(n3r) algorithm for computing the (unique) solution.},
year     = {2019}
}

@article{Dopico2016,
  title   = {Projection methods for large-scale T-Sylvester equations},
  author  = {Dopico, Froil{\'a}n and Gonz{\'a}lez, Javier and Kressner, Daniel and Simoncini, Valeria},
  journal = {Mathematics of Computation},
  volume  = {85},
  number  = {301},
  pages   = {2427--2455},
  year    = {2016}
}

@article{Hadamard1893,
  author = {Hadamard, J.},
  title = {Résolution d'une question relative aux déterminants.},
  journal = {Bull. Sci. Math},
  volume = {17},
  pages = {30--31},
  year={1893}
}

@book{Seber2002,
  author    = {Seber, G. and Lee, A.},
  title     = {Linear Regression Analysis},
  publisher = {John Wiley and Sons},
  year      = {2002}
}

@misc{Alman2020,
      title={A Refined Laser Method and Faster Matrix Multiplication},
      author={Josh Alman and Virginia Vassilevska Williams},
      year={2020},
      eprint={2010.05846},
      archivePrefix={arXiv},
      primaryClass={cs.DS}
}

@misc{Peng2021,
      title={Solving Sparse Linear Systems Faster than Matrix Multiplication},
      author={Richard Peng and Santosh Vempala},
      year={2021},
      eprint={2007.10254},
      archivePrefix={arXiv},
      primaryClass={cs.DS}
}

@misc{WellingXXXX,
  author = {Max Welling},
  title = {The Kalman Filter},
  howpublished = {Lecture Note},
}